Top universities will price out poor students with a five-fold hike to tuition fees if ministers give them free rein over what they charge, an influential education charity warns today.

The Sutton Trust commissioned research into how much degree courses would cost if universities did not have to keep fees to the current cap of £3,290 per year.

Removing the cap and creating a free market – allowing universities to charge whatever they wish – is one option being considered by a cross-party review into higher education.

The review, led by the former BP chief executive Lord Browne, is likely to be published in just over a week and will lead to dramatic changes in English higher education as early as next year. The Observer reported on Sunday that Browne will recommend that universities be allowed to keep all the income from tuition fees up to an annual level of £10,000. The current cap is £3,290. He is expected to recommend that they be allowed to cross that threshold if they pay a rising proportion of the additional income into a central fund.

The government says the current system is "not fit for purpose".

The Sutton Trust study analysed how much 20 universities charge undergraduates from outside the European Union, and how much they charge postgraduates from all countries. Universities are allowed to charge whatever they like to these two groups, so a free market already exists.

The researchers found that at several of the most prestigious universities, fees for non-EU undergraduates are at least five times higher than those for UK students. At University College London (UCL), overseas students pay £16,725 a year for a degree in physics, business or computer science, compared to the £3,290 charged to UK students.

The researchers, from the Centre for Economic Performance at the London School of Economics, found that the most prestigious institutions charge twice as much as lower-ranked universities. Derby University charges around half what UCL does for a business degree at £8,500, for example.

The same applies to postgraduate fees. While Imperial College London charges £21,550 for a master's in computer science, Derby charges £8,950.

Professor Steve Machin, one of the researchers, said the fees charged to postgraduates and overseas undergraduates "provide an indication of what could happen if the financial charges for undergraduate courses are allowed to vary more than they currently do". Undergraduate fees could "rapidly increase, particularly for those universities with the highest academic reputations and particularly for degree courses, such as business, with the highest returns".

Machin said: "There are obvious concerns that such large variations might deter students from less privileged backgrounds. Certain universities and courses with the highest financial return may become off-limits for less privileged students."

Another option being considered by Browne is to allow universities to admit more students from overseas, but to keep the number of students from the UK the same.

The researchers said that by 2015, this would mean that 10% of all undergraduates studying in England and 50% of postgraduates would be from outside the EU.

Machin warned universities could give greater priority to recruiting international students than to seeking the brightest students from low-income families in the UK. "Part of the solution may be to introduce financial incentives for universities to recruit poorer students," he added.

The National Union of Students (NUS) said the removal of the cap would be "a nightmare for students and their families".

"Top-up fees were tripled four years ago and the public will not tolerate a further hike," Aaron Porter, the NUS president, said. "Fortunately a great many politicians have pledged to oppose higher fees and we will hold them to their promise to prevent the emergence of a damaging and destructive market in fees that would entrench privilege and benefit a narrow elite."

Sally Hunt, general secretary of the lecturers' trade union the University and College Union, said Browne "must look seriously at the idea of taxing big business for the substantial benefits it gains from a plentiful supply of graduates".

But the most prestigious universities said that while they were committed to increasing the proportion of students from low-income families on their campuses, they had to find ways to boost their income.

Wendy Piatt, director general of the prestigious Russell Group of universities, said: "Many universities actually make a loss in recruiting many home students, particularly for expensive science courses, because of underfunding from the government and the fact that we are not allowed to ask graduates to make a higher contribution to those costs.

"The current system is not sustainable, particularly if we are facing further damaging cuts. We simply cannot continue to provide the high quality education that our students need – never mind take on higher numbers of students as the Sutton Trust urges – without asking them to make a larger financial contribution."

A spokesperson for the Department for Business Innovation and Skills said ministers would judge Browne review's proposals "against the need to take into account the impact on student debt, ensure a properly funded university sector, improve the quality of teaching, advance scholarship, increase social mobility and attract a higher proportion of students from disadvantaged backgrounds".